1. What if your car has a steering lock? What would they do to drive it?

This is at bottom a mixed conditional, but disguised somewhat by the two-question format:

1a. If your car has a steering lock, what would they do to drive it?

In the first question, the speaker uses 'has' to give an impression of immediacy. In the second question, however, 'will' would give too great an impression of immediacy, as if the thieves were breaking into your car this very second. So the speaker reverts to the usual 'would', which is used to express a remote or imaginary event.

This would be the standard form:

1b. If your car had a steering lock, what would they do to drive it?

2. This is pretty much what I would expect from a member.

The 'would' softens the comment, by making it more 'remote'. If you said 'this is what I expect from a member', it might seem a little too forthright, as if there were no doubt at all about how members behave.

The company is proposing the $1.5 billion private-sector venture for profit. An underwater cable would bring the power to the city, where the company wants to sell the power.

1. An underwater cable would bring the power to the city, where the company wants to sell the power. ('Wants' is compatible with 'would' ? How come not 'wanted'? Although I know it sounds wrong.)

– 'Bringing the power' is conditional. You can think of it like this: "(if the venture went ahead,) an underwater cable would bring the power to the city".

'Wants' is indicative, because whether or not the venture goes ahead, the company still wants to sell the power in the city. The 'wanting' isn't conditional on anything.

2. An underwater cable will bring the power to the city, where the compants wants to sell the power. (So this one is no good for that context? I'm saying he is going to begin the construction?)

– The 'will' could imply that the plan is going ahead. On the other hand, 'will' is sometimes used for something that is still only at the planning stage. You can think of it as: '(if the venture goes ahead,) an underwater cable will bring the power to the city'.

3. So, dying of thirst. would probably feel pretty much like the hangover that finally bloodily kills you. (Is 'would' a conditional here? How come I can use 'kills'? Why not 'killed' ?

There's no real connection between 'dying of thirst' and the hangover: it's a comparison. You can use 'killed' to make the hangover seem more remote, or 'kills' to make it sound definite. But it's a stylistic choice: in reality, a hangover has no such power.

4. What is it exactly that you would like me to do? (Is this a conditional? What would the other part be?)

'What would you like me to do' is a polite (remote) form of 'what do you want me to do'.

5. What is it exactly that you will like me to do? (Is the meaning of this one the same as #4 except this one is asking for a more concrete answer?)

No, the 'will' here would be a future tense. You're very unlikely to hear it, though.